Description will be made taking X-rays as an example of radiation. The object may be a mounted substrate, a through hole/pattern/solder joint of a multilayer substrate, an electronic component before mounting such as an integrated circuit (IC) arranged on a palette, a casting such as of metal, or a molded article such as a videocassette recorder. Specifically, it is used for inspection of electronic components (eg inspection of wiring on substrates, and inspection of BGA (Ball Grid Array), solder joints, voids) and for inspection of internal defects of these objects.
With a CT (Computed Tomography) apparatus known conventionally, as shown in FIG. 1, an object O is placed on a rotary stage S between an X-ray tube T (radiation emitting device) and an X-ray detector D (radiation detecting device) arranged opposite each other. The object O placed on the rotary stage S is rotated by rotating the rotary stage S about an axis of rotation Ax extending perpendicular to the surface of the rotary stage S. By rotating the object O about the axis of rotation Ax in this way, projection images of the object O are obtained from various angles, and a three-dimensional image is calculated by reconstructing these projection images.
When conducting X-ray inspection by tomography of an object having a very fine structure such as Ball Grid Array (BGA) or wiring, it is necessary to carry out radiography with an increased enlargement ratio. In order to increase the enlargement ratio, however, it is necessary to carry out radiography with the radiation source represented by the X-ray tube and the object brought close to each other. In the case of the object having a large planar shape, there arises a possibility that the X-ray tube and the object interfere each other. As a result, in order to avoid interference, the enlargement ratio cannot be increased too much.
So, planar CT (PCT: Planar Computed Tomography) is known, which carries out tomography, as shown in FIG. 2, with the X-ray tube T and X-ray detector D arranged in an oblique direction inclined by lamino angle from the axis of rotation Ax to avoid interference with the object O. Also for an X-ray fluoroscopic apparatus having no rotating mechanism for a stage, there is a method of realizing PCT, in which, as shown in FIG. 3, a stage S with an object O placed thereon is put to parallel translation to describe a circular path on a plane (level plane in FIG. 3) perpendicular to an axis of rotation Ax, and driving an X-ray detector D to revolve about the same axis of rotation Ax synchronously with the movement of stage S. See Patent Document 1: Japanese Unexamined Patent Publication No. 2010-2221, and Patent Document 2: Japanese Patent No. 3694833, for example.
Since, in the radiographing method of FIG. 3, the stage and the X-ray detector have drive mechanisms independent of each other, mechanisms and control are required to realize highly precise positioning and synchronization in order to acquire ideal tomographic scan paths, which results in increased cost. So, even where a disagreement occurs between actual scan paths and ideal scan paths, there is a method of calculating actual scan paths with high precision by calibration (correction) with a phantom for correction, and maintaining them as correction parameters for reconstruction. See Patent Document 3: Japanese Patent No. 4415762, for example. The correction parameter calculation at this time is the same problem setting as the camera calibration known in the field of computer vision, and a method such as Bundle Adjustment is known as a calculation algorithm.
The Bundle Adjustment method is a technique of calculating, from characteristic points extracted from images, three-dimensional coordinates of the characteristic points and parameters of a geometric model at the time of radiography by nonlinear optimization operation. Since repetitive operations are carried out at this time, computation time may become long due to various conditions such as a method of setting initial values, the number of characteristic points, the number of frames and an estimated number of parameters. So, methods of reducing computation time have been proposed. See Patent Document 4: Japanese Unexamined Patent Publication No. 2007-48068, and Patent Document 5: Japanese Unexamined Patent Publication No. 2009-14629, for example.
Patent Document 4, ie Japanese Unexamined Patent Publication No. 2007-48068, tackles as follows the problem that speeding up of an operation using conventional Jacobian matrix being a sparse matrix including many zeros cannot be applied directly because of an increase of unknown parameters when there are two or more types (such as point pattern and square pattern) in the amount of characteristic extracted from images. That is, the unknown parameters are divided into three or more and are put into a matrix form enabling a speed-up of operation, which are calculated by stages to realize shortening of the computation time.
Patent Document 5, ie Japanese Unexamined Patent Publication No. 2009-14629, tackles as follows the problem that the convergence of nonlinear optimization operation becomes poor and exerts an adverse influence on parameter calculation accuracy and computation time when an error occurs in matching between the frames of characteristic points extracted from images or when inappropriate characteristic points are extracted. That is, it seeks to attain a high precision and high speed of the nonlinear optimization operation by applying a robust estimating method (LmedS method or RANSAC method) which removes outliers at the time of evaluation function calculation, thereby to inhibit the influence of outliers.